This paper focuses on 3-D dynamic modeling of a transport quadrotor with cable in the presence of load generating stochastic forces. In many practical cases, we are dealing with payloads that generate oscillating forces with random amplitude and frequency by their inherent dynamics or interacting with the environment. These forces can greatly affect the dynamics of the transport system. The innovation of the present study is to consider these forces and show their impact on quadrotor’s dynamics. Furthermore, in order to make the model more compatible with the real system, it is assumed that the connection point of cable and quadrotor is not located on the center of gravity of flying vehicle and the cable's inertia is considered in the modeling process. To this end, the systems’ equations of motion are derived based on both Euler-Lagrange and Newton-Euler methods. After obtaining equations of motion, the verification of the model is investigated in three steps. In the first step, by performing simulation, the validity of the nonlinear model is investigated and dynamical analysis is expressed. In the next step, by evaluating the structure of the model, it is shown that the equations of motion satisfy some structural features of a desirable dynamic model. Then, by setting some parameters and variables to zero, it is shown that simpler models provided in some references can be achieved from this comprehensive model. At the end, the conclusion of this work is presented.